It is well-known that the human visual system is adapted to the statistical structure of natural scenes. Yet there are important classes of images - for example, medical images - that are not natural scenes, and therefore, that are expected to have statistical properties that deviate from the class of images that shaped the evolution and development of human vision. Here, focusing on structural brain MRI images, we quantify and characterize these deviations in terms of a set of local image statistics to which human visual sensitivity has been well-characterized, and that has previously been used for natural image analysis. We analyzed MRI images in multiple databases including T1-weighted and FLAIR sequence types, and simulated MRI images based on a published image simulation procedure for T1 images, which we also modified to generate FLAIR images. We first computed the power spectra of MRI images; spectral slopes were in the range -2.6 to -3.1 for T1 sequences, and -2.2 to -2.7 for FLAIR sequences. Analysis of local image statistics was then carried out on whitened images. For all of the databases as well as for the simulated images, we found that the three-point correlations contributed substantially to the differences between the "texture" of randomly selected ROIs. The informative nature of three-point correlations for brain MRI was greater than for natural images, and also disproportionate to human visual sensitivity. As this finding was consistent across databases, it is likely to result from brain geometry at the scale of brain MRI resolution, rather than characteristics of specific imaging and reconstruction methods.